Nau Abstract Arbitrage and Rational Choice Over the last 50 years, the theory of rational choice has provided the foundation for much of the most important and influential research in the social and economic sciences, including work in statistical decision theory, game theory, social choice, microeconomics, financial economics, and political science. Rational choice theory predicts or prescribes socioeconomic behavior by starting from a mathematical model of the perfectly rational individual-the `expected utility maximizer` - but modeling approach has become increasingly controversial in recent years for a variety of reasons. First, there is abundant empirical evidence that real individuals do not display the type of rationality (e.g., completeness and consistency of preferences) that the theory requires, while the impressive talents that they do have (e.g., pattern recognition, inductive reasoning, creativity, leadership) play almost no role in theory. Second, many of our familiar democratic and market institutions (speculative trade, voting systems, organization structures) are hard to reconcile with the assumption that every individual has a complete mental model of the world and consistent preferences with respect to everything that might happen in it. Third, some of the technical elements of standard rational choice theory are now regarded to be untenable even as idealizations of intelligent, self-interested behavior. This project develops a alternative formulation of rational choice that resolves many of the paradoxes and puzzles of the standard theory and leads to a deeper unification of the theories of decisions under uncertainty, games of strategy, and competitive markets. In place of the standard assortment of preference axioms and equilibrium concepts, there is a single axiom of rationality, namely that there should be no unexploited arbitrage opportunities - i.e., no free lunches or money pumps. This no-arbitrage definition of rationality is inherently group-centered rather than individual-centered, and it does not depend on the assumption that every individual has a complete decision model. Rather, it provides a framework in which the incomplete decision models of bondedly-rational individuals can combine to form a more complete model when they interact with each other. As such, it admits a more natural role for institutions and organizations, namely that they aggregate the knowledge, expertise, and creativity of many individuals in order to solve complex problems. The project will develop new arbitrage-based models of sequential decisions, strategic reasoning, and asset pricing, as well as explore some of the larger foundational and methodological issues surrounding the theory of rational choice.
